President Obama and Russian President Dmitri Medvedev officially reset relations between their two countries today after eight years of increasing testiness and lack of cooperation.

Top of the new agenda: An agreement to quickly and dramatically reduce the number of long-range nuclear weapons on both sides, thousands of which remain on hair-trigger alert.

From the joint statement released by Obama and Medvedev after their meeting in London today, before tomorrow's G-20 talks:

"We, the leaders of Russia and the United States, are ready to move beyond Cold War mentalities and chart a fresh start in relations between our two countries. In just a few months we have worked hard to establish a new tone in our relations. Now it is time to get down to business and translate our warm words into actual achievements of benefit to Russia, the United States, and all those around the world interested in peace and prosperity....

"We agreed to pursue new and verifiable reductions in our strategic offensive arsenals in a step-by-step process, beginning by replacing the Strategic Arms Reduction Treaty with a new, legally-binding treaty....

"We intend to carry out joint efforts to strengthen the international regime for nonproliferation of weapons of mass destruction and their means of delivery...

"We agreed that al-Qaida and other terrorist and insurgent groups operating in Afghanistan and Pakistan pose a common threat to many nations, including the United States and Russia. We agreed to work toward and support a coordinated international response with the U.N. playing a key role."

It's a pretty dramatic shift. Former president George W. Bush's relationship with former Russian president Vladimir Putin was characterized by an unfortunate combination of naivete and cockiness, and ended up remarkably bitter, confrontational and ineffectual.

Before today's meeting, an unnamed senior administration official described Obama's approach this way to ABC's Jake Tapper: "Nobody's going to be looking into anybody's soul."

It was a reference to Bush's first meeting with Putin, at which Bush famously declared that he had looked into the former KGB officer's eyes, had gotten "a sense of his soul," and had "found him to be very straightforward and trustworthy."

Putin proceeded to become increasingly authoritarian, consolidating power both inside and outside Russia. Bush responded by provoking Putin with a proposed missile defense installations in Eastern Europe and a push to include former Soviet republics in NATO. Putin arguably responded by invading Georgia.

Medvedev, for his part, wrote in a Washington Post op-ed yesterday that "relations soured because of the previous U.S. administration's plans -- specifically, deployment of the U.S. global missile defense system in Eastern Europe, efforts to push NATO's borders eastward and refusal to ratify the Treaty on Conventional Armed Forces in Europe."

But, he wrote: "Neither Russia nor the United States can tolerate drift and indifference in our relations."

"[W]hat we've seen over the last several years is drift in the U.S.-Russian relationship," he said. "There are very real differences between the United States and Russia, and I have no interest in papering those over. But there are also a broad set of common interests that we can pursue. Both countries, I believe, have an interest in reducing nuclear stockpiles and promoting nuclear nonproliferation. Both countries have an interest in reducing the threat of terrorism. Both countries have an interest in stabilizing the world economy. Both countries have an interest in finding a sustainable path for energy and dealing with some of the threats of climate change that we've discussed.

"So, on a whole range of issues, from Afghanistan to Iran to the topics that will be consuming most of our time here at the G20, I think there's great potential for concerted action. And that's what we will be pursuing.

"Now, as has I think been noted in the press, a good place to start is the issue of nuclear proliferation. And one of the things that I've always believed strongly is that both the United States and Russia and other nuclear powers will be in a much stronger position to strengthen what has become a somewhat fragile, threadbare nonproliferation treaty if we are leading by example and if we can take serious steps to reduce the nuclear arsenal.

"I think people on both sides of the Atlantic understand that as much as the constant cloud, the threat of nuclear warfare has receded since the Cold War, that the presence of these deadly weapons, their proliferation, the possibility of them finding their way into the hands of terrorists, continues to be the gravest threat to humanity. What better project to start off than seeing if we can make progress on that front. I think we can."

In his remarks after meeting with Medvedev, Obama announced that he will travel to Moscow in July.

Peter Baker and Helene Cooper wrote in today's New York Times that "American and Russian officials have privately indicated that they could agree to reducing their stockpiles perhaps to about 1,500 warheads apiece, down from the 2,200 allowed under a treaty signed by President George W. Bush....

"[N]ext year, the two sides envision a more ambitious agreement that could reduce warheads further, even to 1,000, as well as limit delivery vehicles and possibly tactical nuclear weapons....

"Steven Pifer, a former deputy assistant secretary of state under Mr. Bush...., said Mr. Obama's initiative could finally bury the cold-war nuclear legacy. 'It's cleaning up some unfinished business that's been put on hold for the last seven years,' he said."

Michael D. Shear writes for The Washington Post that the joint statement "outlines new areas of planned cooperation while skirting some of the most contentious issues that have soured relations during the past several years.

"They pledged to cooperate on trying to rein in Iran's nuclear ambitions, contain the proliferation of nuclear technology, and fight terrorism in Afghanistan and Pakistan. And they expressed joint concern about North Korea's expected launch of a ballistic missile sometime soon....

"The statement does not attempt to resolve some of the stickiest issues that divide Washington and Moscow, in particular the disagreement over Russia's aggressive actions in the nation of Georgia and the deployment of missile defense equipment in Poland."